Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 91, 2019 - Issue 7: Hammamet Stochastic Analysis 2017
234
Views
1
CrossRef citations to date
0
Altmetric
Articles

Mean-field stochastic control with elephant memory in finite and infinite time horizon

&
Pages 1041-1066 | Received 25 Apr 2018, Accepted 20 Jun 2019, Published online: 02 Jul 2019
 

ABSTRACT

Our purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history. We study both the finite horizon case and the infinite time horizon case.

  • In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem.

  • For infinite horizon, we derive sufficient and necessary maximum principles.

    As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was carried out with support of the Norwegian Research Council, within the research project Challenges in Stochastic Control, Information and Applications (STOCONINF), project number 250768/F20.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,425.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.